A Nice Math Olympiad Algebra Problem | How to solve for X and Y in this Problem ?

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Уравнение от переменной просто решается по теореме Виета и далее простая система уравнений. Ход решения правильный, но не рациональный.

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x+y=a
x^5+y^5=b
fomular to find x.y
5a(xy)^2 + 5a^3(xy) + a^5 - b = 0